A Study On A New Class Of Compound Extreme Value Distribution

The lifetime distribution of serial system is studied in this paper, employing the mixture distribution to depict the lifetime of component which is affected by many factors. Here, the component’s lifetime is independent and identically distributed, and the number of serial component is subjected to a discrete distribution, thus, the lifetime of the serial system follows a new compound extreme value distribution.(1) When the lifetime of the component obeys the mixture exponential distribution, the number of element follows the geometric distribution, the lifetime of the serial system follows the mixed exponential geometric distribution with monotonic decreasing failure rate. In this paper, various properties and the MLE of parameters of the mixed exponential geometric distribution are discussed, the approximate estimates of parameters are obtained by EM algorithm., and parameters of asymptotic variances, covariances and confidence intervals are given.(2) When the lifetime of the component obeys the mixture exponential distribution, the number of element follows the Zero-truncated Poisson distribution, the lifetime of the serial system follows the mixture exponential Poisson distribution. Likewise, many properties and the MLE of parameters of the mixture exponential Poisson distribution are studied, the approximate estimates of parameters are acquired by EM algorithm., and parameters of asymptotic variances, covariances and confidence intervals are given.(3) The paper discusses the generalized Pareto distribution, which is a new extreme value distribution with not consistent decreasing failure rate. In this paper, kinds of properties and the MLE of parameters of the generalized Pareto distribution are discussed, the approximate estimates of parameters are deduced by EM algorithm, and parameters of asymptotic variances, covariances and confidence intervals are given.